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At this stage Diana, Arthur and Alice, which was favourite at different stages for Kate and William’s babies, are the 12/1 front runners.

Betfair Spokeswoman Katie Baylis

"Their Royal Highnesses have appreciated all of the support they have received from people around the world since their wedding in May and are delighted to be able to share this happy news with the public."

As with the Duke and Duchess of Cambridge the baby announcement has sent shockwaves across the world and fuelled rumours as to the what the Prince of Wales’ fourth grandchild will be called.

Betfair Spokeswoman Katie Baylis said: “Meghan’s loose coat at Princess Eugenie’s wedding on Friday led to speculation that an announcement was imminent and now that we have it, the Royal Baby name game starts.

“At this stage Diana, Arthur and Alice, which was favourite at different stages for Kate and William’s babies, are the 12/1 front runners.

Meghan Markle and Prince Harry have announced they are expecting a baby (Image: GETTY)

Meghan and Harry arriving in Sydney (Image: SPLASH )

“However, with months until the baby is born, those odds will shorten, change and other names will come to the forefront, so watch this space.”

Traditional names remain the most likely possibilities with Charles, Edward or James for a boy and Alice, Elizabeth or Victoria for a girl.

However, Harry and Meghan may be willing to break tradition with bookmakers not “ruling out” a more left-field choice as their child will be seventh-in-line to the throne and extremely unlikely to ever be King or Queen.

Jessica Bridge of Ladbrokes said: “With Meghan’s USA roots it would be remiss of bookmakers to rule out an American moniker featuring somewhere”.

Meghan and Harry have spoke very little about starting a family but in an interview in 2016 the Duchess said she “can’t wait” to start a family.